Solve 3p^4(p^8)(-p^3)=

$$3 p ^ { 4 } ( p ^ { 8 } ) ( - p ^ { 3 } ) =$$

Evaluate

$$-3p^{15}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$3p^{12}\left(-p^{3}\right)$$

Multiply 3 and -1 to get -3.

$$-3p^{12}p^{3}$$

To multiply powers of the same base, add their exponents. Add 12 and 3 to get 15.

$$-3p^{15}$$

Differentiate w.r.t. p

$$-45p^{14}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}p}(3p^{12}\left(-p^{3}\right))$$

Multiply 3 and -1 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}p}(-3p^{12}p^{3})$$

To multiply powers of the same base, add their exponents. Add 12 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}p}(-3p^{15})$$

The derivative of ax^{n} is nax^{n-1}.

$$15\left(-3\right)p^{15-1}$$

Multiply 15 times -3.

$$-45p^{15-1}$$

Subtract 1 from 15.

$$-45p^{14}$$